its a slow burn, but Clannad(more specifically in S2(after story)).
plastic memories
your lie in april
A Silent Voice(this is just a really good movie regardless)
if I recall right Suka Suka(im not typing the full long af name) got me on my first watch to

I could recommend some emotional anime like: Kimi no Na wa., Shingeki no Kyojin, Angel Beats!, Shigatsu wa Kimi no Uso, Violet Evergarden, Guilty Crown.

I think Angel Beats was the only one that actually made me cry, or maybe the only one that made me cry more than once so it managed to burn itself into my memory as the one anime that made me cry. Edgerunners is definitely one that delivers emotional gut punches, but it's so visually pretty and action packed that it doesn't give one much time to process before something else demands one's attention.

Since people above already recommend some popular one, i'll recommend some less popular one.
Maquia : When the Promised Flower Blooms
To Your Eternity
Death Parade
Somali and the Forest Spirit

5 Centimeters per Second (秒速5センチメートル)
Grave of the Fireflies (火垂るの墓)

NEKOPARA OVA

Always Violet Evergarden. Hard cry

Way back then, everyone and their dogs seemed to think Saishuuheiki Kanojo was very good at making people cry. Apparently it hits really hard, but nobody remembers it anymore because it's very old; I myself haven't watched it yet, but it still comes to mind really easily for what you want, so please let me know what you think if you decide to!

Also, if you're taking gratuitous suffering, consider Made in Abyss. It won't necessarily make you cry (though it sure has the potential to make you cry a river), but it also might suck out your soul in the process. Consider yourself warned: it isn't a show for the faint of heart! To a lesser extent, but along the same lines, and also a timeless classic that can often be very off-putting in all sorts of ways: Shinsekai yori (From the New World).

From the recommendations already in the thread, I guess I'd give a strong +1 to Violet Evergarden, Sukasuka, and Shigatsu wa Kimi no Uso (Your Lie in April). On the other hand, Koe no Katachi (A Silent Voice) may not result in tears, but it's a life experience so I'd strongly recommend it anyway.

JoJo first season

As mentioned above, Angel Beats is a hard hitter. While I didn't cry, it has a huge representation for how sad it is.

For me, As someone with a bad relationship history, shows like Ao Haru Ride and Orange got me crying within the first few episodes though nothing inherently sad happens, they remind me of the sugar sweet days of young love and I weep over that. Orange admittedly does have some sadness to it but it's not too bad.

For the very specific audience of people who cry from romance type shows, is LGBT+ friendly, and doesn't mind topics of (Trigger Warning & light Spoiler) > suic*de I personally rewatched Given maybe 8 times over with multiple different people and cried every time. I swear this one actually really is a fair bit sad though.

Fruits Basket!! (the newer anime not the old one)
Violet Evergarden
Maybe Elfen Lied

I have more options but they are manga, not anime

All of the above are very good options ill add my 5 cents, enjoy and bring some handkerchief.

Nana - Relationship drama
Bokura no - sci-fi
Romeo x Juliet- a classic
Kimi ni Todoke - school romance
Ano Hi Mita Hana no Namae wo Bokutachi wa Mada Shiranai - i drop a tear everytime i remember or talkabout it this one hit me hard specially

Voices of a Distant Star and She and Her Cat.

Stein;s Gate.It's a good anime but the twists make you feel angry,sad and mad. May I suggest Death Note for some entertainment as well.

Naruto

Got emotional with some scenes of Eighty-Six

Tenkuu Danzato Skelter Heaven

The consummate weeb in me has been summoned! Couple disclaimers, tho - as I see most of the recommendations that are already here are the well known stuff, I'll try to avoid those. Also, I cry more with Slice of Life than with hard drama, but that's. Just me.

• Someone above mentioned Given. In a word: yes. Unless the person reading is a lgtb+phobe, in which you should feel free to blacklist me and stop reading, this is a heart-wrenching experience. It may have some comedy, but the sad parts hit hard.
• Somehow no one has mentioned Madoka? I spent the last episode in shock and started bawling like a baby at a point, after which I din't stop crying for a good 20 minutes. So, Mahou Shoujo Madoka Magica.
• Udon no Kuni no Kiniro Kemari is mostly found family/kid raising fluff, but man, when it gets sad its devastating.
• Kotarou wa Hitorigurashi is adult fear and pain and amazing and I love it. Local 4 year old will make you very, very sad. I literally watch it when I need a good cry.
• Lastly, Kotoura-san has the hardest start I have ever seen in a romcom, and even after it gets better, it will often dip back into sadness, and it does it in a gut-wrenching manner. Don't let the colors distract you, it is the poster child of "why reading minds would suck".

If aanyone asks I'll drop more reccs :)

Death Parade

Aww sad kitty....Ive had Edgerunners in my towatchlist.
But for me, I have only cried when Jiraya died, the whole Pein arc was incredible and emotional for me.

Saishuu Heiki Kanojo (aka. Saikano) is one of those relatively unknown anime that makes me cry too.

One Piece have the most sad moments.
The shows cannot even compare.
I mean really cry out type of saddest.

Cyberpunk: Edgerunners
Kimi no Suizou wo Tabetai
Koe no Katachi
Shigatsu wa Kimi no Uso
Shingeki no Kyojin
Violet Evergarden

In my eyes Wolf's Rain had a pretty emotional second half of the series. It also had a nice setting and characters. Here is a trailer: https://youtu.be/AXoTxTizh2o

Blood+